Some observations about generalized quantifiers in logics of imperfect information

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Barbero , F 2019 , ' Some observations about generalized quantifiers in logics of imperfect information ' , The Review of Symbolic Logic , vol. 12 , no. 3 , pp. 456-486 . https://doi.org/10.1017/S1755020319000145

Title: Some observations about generalized quantifiers in logics of imperfect information
Author: Barbero, Fausto
Other contributor: University of Helsinki, Theoretical Philosophy

Date: 2019-09
Language: eng
Number of pages: 31
Belongs to series: The Review of Symbolic Logic
ISSN: 1755-0203
DOI: https://doi.org/10.1017/S1755020319000145
URI: http://hdl.handle.net/10138/306693
Abstract: We analyse the two definitions of generalized quantifiers for logics of dependence and independence that have been proposed by F. Engstrom. comparing them with a more general, higher order definition of team quantifier. We show that Engstrom's definitions (and other quantifiers from the literature) can be identified, by means of appropriate lifts, with special classes of team quantifiers. We point out that the new team quantifiers express a quantitative and a qualitative component, while Engstrom's quantifiers only range over the latter. We further argue that Engstrom's definitions are just embeddings of the first-order generalized quantifiers into team semantics. and fail to capture an adequate notion of team-theoretical generalized quantifier, save for the special cases in which the quantifiers are applied to flat formulas. We also raise several doubts concerning the meaningfulness of the monotone/nonmonotone distinction in this context. In the appendix we develop some proof theory for Engstrom's quantifiers.
Subject: 611 Philosophy
Logic
generalized quantifiers
Independence-friendly logic
Team semantics
IF logic
higher order quantifiers
IF logic
logics of dependence and independence
generalized quantifiers
higher order quantifiers
team semantics
DEPENDENCE LOGIC
INDEPENDENCE
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